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math.NT2026
Generalized rank deviations for overpartitions
Kevin Allen, Robert Osburn, Matthias Storzer
We prove formulas for generalized rank deviations for overpartitions. These formulas are in terms of Appell-Lerch series and sums of quotients of theta functions and extend work of…
math.NT2025
Unimodal sequences and mixed false theta functions
Kevin Allen, Robert Osburn
We consider two-parameter generalizations of Hecke-Appell type expansions for the generating functions of unimodal and special unimodal sequences. We then determine their explicit…